Simplify Square Root of 35213

What is the square root of 35213 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√35213 = A√B

Unfortunately, the square root of 35213 cannot be simplified. Thus, here is the answer to the square root of 35213 in its simplest form:

√ 35213 = √ 35213

Here are two different methods we used to determine why the square root of 35213 cannot be simplified.

1) To be able to simplify the square root of 35213, one of the factors of 35213 other than 1 must be a perfect square. The factors of 35213 are 1, 23, 1531, and 35213. Since none of these factors are perfect squares, the square root of 35213 cannot be simplified.

2) To be able to simplify the square root of 35213, all the prime factors of 35213 cannot be unique. When we did prime factorization of 35213, we found that 23 x 1531 equals 35213. Since all the prime factors are unique, the square root of 35213 cannot be simplified.

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